The Standard Model (SM) predicts that $\mathrm{\Delta }{A}_{CP}$, the difference between the direct $CP$ asymmetries for the modes $B^{+}\to {\pi }^0{K}^{+}$ and $B^0\to {\pi }^{-}{K}^{+}$ that are related by a weak isospin, should be close to zero. There has been a recent claim by the LHCb Collaboration that the measured value of $\mathrm{\Delta }{A}_{CP}$ shows an uncomfortable tension with the SM prediction, almost at the $8\sigma$ level. Motivated by this claim, we critically reexamine the data on all the $B\to \pi K$ modes, including the $CP$ asymmetries and $CP$-averaged branching fractions. From a combined Bayesian analysis with the topological amplitudes and their phases as the free parameters, we find that the best-fit region has a large overlap with the parameter space favored in the SM, albeit with some enhancement for the electroweak penguin and the color-suppressed tree amplitudes; consistent with the findings of earlier studies. We find that in this SM-like region, $\mathrm{\Delta }{A}_{CP}$ is more than $5\sigma$ away from zero and the tension with the global average, as well as the LHCb result, is within $2\sigma$. Thus, we conclude that there is not yet enough motivation to go beyond the SM.

• Received 5 July 2021
• Revised 23 September 2021
• Accepted 1 November 2021

DOI:https://doi.org/10.1103/PhysRevD.104.095025

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Published by the American Physical Society